Question

Consider the two regression lines 3x+2y =26 and 6x+y=31,(a)Find the mean value and correlation conefficient between x and y.(b) if the varianceof y is 4,Find the S.D .of x

Answer 1

$3x+2y=26$...i

$6x+y=31$ ....ii balancing both y by multiplying by 2

$3x+2y=26$

$12x+2y=62$

Deducting the two equations

$-9x=-36$

$x=4$

replacing the value of x to get y

$6(4)+y=31$

$y=31-24$

$y=7$

Since the point of intersection of the two correlation lines is x,y then the point is (4,7)

Then the mean of x is 4 and y is 7.

Assuming 3x+2y-26=0 is the regression equation.

2y=-3x+26

y=-3/2x+13

Hence the correlation coefficient of y to x is -3/2

Hence the correlation coeffient of x to y is -1/6